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 Critical points and Warped product metrics Bull. Korean Math. Soc. 2004 Vol. 41, No. 1, 117-123 Published online March 1, 2004 Seungsu Hwang, Jeongwook Chang Chung-Ang University and Konkuk University Abstract : It has been conjectured that, on a compact orientable manifold $M$, a critical point of the total scalar curvature functional restricted the space of unit volume metrics of constant scalar curvature is Einstein. In this paper we show that if a manifold is a $3$-dimensional warped product, then $(M,g)$ cannot be a critical point unless it is isometric to the standard sphere. Keywords : total scalar curvature functional, critical point equation, Einstein metric MSC numbers : 52C25 Downloads: Full-text PDF